Algebra.Structures.BezoutDomain
Description
Representation of Bezout domains. That is non-Noetherian analogues of principal ideal domains. This means that all finitely generated ideals are principal.
- class IntegralDomain a => BezoutDomain a where
- toPrincipal :: Ideal a -> (Ideal a, [a], [a])
- propBezoutDomain :: (BezoutDomain a, Eq a) => Ideal a -> a -> a -> a -> Property
- intersectionB :: (BezoutDomain a, Eq a) => Ideal a -> Ideal a -> Ideal a
- intersectionBWitness :: (BezoutDomain a, Eq a) => Ideal a -> Ideal a -> (Ideal a, [[a]], [[a]])
- solveB :: (BezoutDomain a, Eq a) => Vector a -> Matrix a
Documentation
class IntegralDomain a => BezoutDomain a whereSource
Bezout domains
Compute a principal ideal from another ideal. Also give witness that the principal ideal is equal to the first ideal.
toPrincipal <a_1,...,a_n> = (<a>,u_i,v_i) where
sum (u_i * a_i) = a
a_i = v_i * a
Methods
toPrincipal :: Ideal a -> (Ideal a, [a], [a])Source
Instances
| (EuclideanDomain a, Eq a) => BezoutDomain a |
propBezoutDomain :: (BezoutDomain a, Eq a) => Ideal a -> a -> a -> a -> PropertySource
intersectionB :: (BezoutDomain a, Eq a) => Ideal a -> Ideal a -> Ideal aSource
Intersection without witness.
intersectionBWitness :: (BezoutDomain a, Eq a) => Ideal a -> Ideal a -> (Ideal a, [[a]], [[a]])Source
Intersection of ideals with witness.
If one of the ideals is the zero ideal then the intersection is the zero ideal.